Comprehension
Two vertical light poles of height 22 m and 16 m stand on the opposite sides of a 20 m wide road as shown below in the figure. Two ladders of length \( l_1 \) and \( l_2 \) are placed from a common point R on the road at a distance of x m from the smaller pole. Based on the above information, answer the following questions :
Question: 1

Express \( p(x) = l_1^2 + l_2^2 \) in terms of x.

Updated On: Jul 4, 2026
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Question: 2

Find \( p'(x) \).

Updated On: Jul 4, 2026
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Question: 3

Using integration, find the area of region OAC, in which children are allowed to play games like cricket, football.

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Question: 4

If the 22 m long pole is also replaced by a 16 m long pole, at what distance from either pole should the ladders be kept so that the sum of squares of lengths of ladders needed to reach the top of the pole is minimum ?

Updated On: Jul 4, 2026
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